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US3649825A
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Apparatus for function generation by linear interpolation
Assignee: ZF International UK Ltd
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Filing: 1969-11-25
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Granted: 1972-03-14
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Expires: 1989-11-25
Abstract
Abstract The invention relates to an apparatus for generating a mathematical function of the type y f(x) by linear interpolation between two values y1, y2 which are known for two values x1, x2. The apparatus includes two function generators respectively producing values y1, y2. Associated with each function generator is an interpolation function generator. The interpolation function generators produce, for a value of x lying between x1 and x2 signals corresponding to (x2-x)/(x2-x) and (x-x1)/(x2-x1) respectively.
Inventors
- 👤 Robert Graham Burrage
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-25 06:40
CPC Classifications
G; G06; G06G; G06G7/00; G06G7/12; G06G7/26; G06G7/28; G06G7/30
Claims Analysis
Total Claims: 11
Claim 1
Independent Claim
177 words
An apparatus for generating a mathematical function by linear interpolation comprising at least first and second function generators for producing on receipt of signals corresponding to x1 and x2 electrical output signals corresponding to y1 f(x1) and y2 f(x2) respectively, where x1 and x2 are previously determined values of x, at least first and second interpolation function generators each of which is associated with a corresponding one of the function generators, the said interpolation function generators producing, on receipt of two input signals corresponding to a value of x lying between x1 and x2, electrical signals corresponding to (x2 - x)/(x2 - x1) and (x - x1)/(x2 x1) respectively at least first and Second multiplying circuits having as input signals the output signals of the respective associated function generators and interpolation function generators, for producing electrical signals proportional to the products of the output signals of each function generator and each corresponding interpolation function generator, and an adding circuit for producing an output signal corresponding to the sum of the signals produced by the said multiplying circuits.
Claim 2
Independent Claim
177 words
An apparatus for generating a mathematical function by linear interpolation comprising at least first and second function generators for producing on receipt of signals corresponding to x1 and x2 electrical output signals corresponding to y1 f(x1) and y2 f(x2) respectively, where x1 and x2 are previously determined values of x, at least first and second interpolation function generators each of which is associated with a corresponding one of the function generators, the said interpolation function generators producing, on receipt of two input signals corresponding to a value of x lying between x1 and x2, electrical signals corresponding to (x2 - x)/(x2 - x1) and (x - x1)/(x2 x1) respectively at least first and Second multiplying circuits having as input signals the output signals of the respective associated function generators and interpolation function generators, for producing electrical signals proportional to the products of the output signals of each function generator and each corresponding interpolation function generator, and an adding circuit for producing an output signal corresponding to the sum of the signals produced by the said multiplying circuits.
Claim 3
Dependent Claim
64 words
An apparatus as claimed in claim 1 in which the input to each interpolation function generator comprises first and second signals of equal magnitude and opposite polarity and each interpolation function generator includes means for generating a pair of voltages which are respective functions of the said two input signals and each interpolation function generator includes means for summing the said pair of voltages.
Claim 4
Dependent Claim
26 words
An apparatus as claimed in claim 2 which includes means for causing all said signals produced by the interpolation function generators to have the same polarity.
Claim 5
Dependent Claim
47 words
An apparatus as claimed in claim 2 which includes means for causing the output signal of each interpolation function generator to have a peak level at a predetermined value of x, and which also includes means for causing the said peak output levels to be substantially identical.
Claim 6
Dependent Claim
57 words
An apparatus as claimed in claim 4 in which each interpolation function generator includes a first regulating means for causing the said peak output level to occur when the value of the signal input to the said interpolation function generator corresponds to the said previously determined value of x forming the input to the associated function generator.
Claim 7
Dependent Claim
36 words
An apparatus as claimed in claim 5 in which the said first regulating means comprises a rectifying means which receives the first of the said two input signals and biasing means associated with the rectifying means.
Claim 8
Dependent Claim
28 words
An apparatus as claimed in claim 4 which includes means for causing the output signal of each interpolation function generator to be zero at predetermined values of x.
Claim 9
Dependent Claim
48 words
An apparatus as claimed in claim 7 in which each interpolation function generator includes a second regulating means for causing the said output signals to be zero at the said previously determined values of x respectively providing the inputs to the next preceding and next subsequent function generators.
Claim 10
Dependent Claim
56 words
An apparatus as claimed in claim 8 in which the said second regulating means comprises rectifying means which receives the second of the said two input signals, biasing means associated with the rectifying means and means for varying the value of the voltage which is a function of the first of the said two input signals.
Claim 11
Dependent Claim
40 words
An apparatus as claimed in claim 1 in which each function generator produces an electrical signal corresponding to a value of y when the said value of y is a function of one or more variables in addition to x.
References Cited (Backward Citations)
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US3506810A
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US3538319A
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1975-03-14 | 1975-09-13 | 1976-03-14 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1979-03-14 | 1979-09-13 | 1980-03-14 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 1983-03-14 | 1983-09-13 | 1984-03-14 | $7700.00 | Window Closed / Lapsed |